Bayesian model-based cluster analysis for predicting macrofaunal communities

To predict macrofaunal community composition from environmental data a two-step approach is often followed: (1) the water samples are clustered into groups on the basis of the macrofauna data and (2) the groups are related to the environmental data, e.g. by discriminant analysis. For the cluster analysis in step 1 many hard, seemingly arbitrary choices have to be made that nevertheless influence the solution (similarity measure, clustering strategy, number of clusters). The stability of the solution is often of concern, e.g. in clustering by the program. In the discriminant analysis of step 2 it can occur that a water sample is misclassified on the basis of the environmental data but on further inspection happens to be a borderline case in the cluster analysis. One would then rather reclassify such a sample and iterate the two steps. Bayesian latent class analysis is a flexible, extendable model-based cluster analysis approach that recently has gained popularity in the statistical literature and that has the potential to address these problems. It allows the macrofauna and environmental data to be modelled and analyzed in a single integrated analysis. An exciting extension is to incorporate in the analysis prior information on the habitat preferences of the macrofauna taxa such as is available in lists of indicator values. The output of the analysis is not a hard assignment of water samples to clusters but a probabilistic (fuzzy) assignment. The number of clusters is determined on the basis of the Bayes factor. A standard feature of the Bayesian method is to make predictions and to assess their uncertainty. We applied this approach to a data set consisting of 70 water samples, 484 macrofauna taxa and four environmental variables for which previously a five cluster solution had been proposed. The standard for Bayesian estimation, the Gibbs sampler, worked fine on a subset with only 12 selected taxa but did not converge on the full set with 484 taxa. This is due to many configurations in which the assignment probabilities are all very close to either 0 or 1. This convergence problem is comparable with the local optima problem in classical cluster optimization algorithms, including the EM algorithm used in Latent Gold, a Windows program for latent class analysis. The convergence problem needs to be solved before the benefits of Bayesian latent class analysis can come to fruition in this application. We discuss possible solutions.